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Article

Stochastic Volatility and GARCH: Do Squared End-of-Day Returns Provide Similar Information?

1
School of Mathematics and Statistics, University of Sydney, Sydney, NSW 2006, Australia
2
Department of Finance, Asia University, Wufeng, Taichung 41354, Taiwan
3
School of Business and Law, Edith Cowan University, Joondalup 6027, Australia
J. Risk Financial Manag. 2020, 13(9), 202; https://doi.org/10.3390/jrfm13090202
Received: 19 June 2020 / Revised: 1 September 2020 / Accepted: 2 September 2020 / Published: 7 September 2020
(This article belongs to the Collection Volatility Modelling and Forecasting)
The paper examines the relative performance of Stochastic Volatility (SV) and GARCH(1,1) models fitted to twenty plus years of daily data for three indices. As a benchmark, I use the realized volatility (RV) for the S&P 500, DOW JONES and STOXX50 indices, sampled at 5-minute intervals, taken from the Oxford Man Realised Library. Both models demonstrate comparable performance and are correlated to a similar extent with the RV estimates, when measured by OLS. However, a crude variant of Corsi’s (2009) Heterogenous Auto-Regressive (HAR) model, applied to squared demeaned daily returns on the indices, appears to predict the daily RV of the series, better than either of the two base models. The base SV model was then enhanced by adding a regression matrix including the first and second moments of the demeaned return series. Similarly, the GARCH(1,1) model was augmented by adding a vector of demeaned squared returns to the mean equation. The augmented SV model showed a marginal improvement in explanatory power. This leads to the question of whether we need either of the two standard volatility models, if the simple expedient of using lagged squared demeaned daily returns provides a better RV predictor, at least in the context of the indices in the sample. The paper thus explores whether simple rules of thumb match the volatility forecasting capabilities of more sophisticated models. View Full-Text
Keywords: stochastic volatility; GARCH(1,1); S& P500; DOWJONES 50; RV 5 min; HAR model; demeaned daily squared returns stochastic volatility; GARCH(1,1); S& P500; DOWJONES 50; RV 5 min; HAR model; demeaned daily squared returns
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MDPI and ACS Style

Allen, D.E. Stochastic Volatility and GARCH: Do Squared End-of-Day Returns Provide Similar Information? J. Risk Financial Manag. 2020, 13, 202. https://doi.org/10.3390/jrfm13090202

AMA Style

Allen DE. Stochastic Volatility and GARCH: Do Squared End-of-Day Returns Provide Similar Information? Journal of Risk and Financial Management. 2020; 13(9):202. https://doi.org/10.3390/jrfm13090202

Chicago/Turabian Style

Allen, David E. 2020. "Stochastic Volatility and GARCH: Do Squared End-of-Day Returns Provide Similar Information?" Journal of Risk and Financial Management 13, no. 9: 202. https://doi.org/10.3390/jrfm13090202

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